14.3. Wing downwash

Fig. 14.4 Wing downwash

As it is known, the vortex sheet is formed behind a lifting surface which creates a downwash. This downwash reduces true angle of attack of a lifting surface located back, that should be taken into account at calculation of its lift and moment characteristics.

Let's consider the case of the normal configuration, when tail unit is located behind the wing. The wing repels air downwards with some speed at creation of lift. Due to it, flow incoming onto horizontal tail downwashes downwards on some angle , which is called as angle of downwash (Fig. 14.4). The downwash behind a wing influences onto the aerodynamic characteristics of all aircraft parts located behind the wing. First of all wing downwash influences onto the aerodynamic characteristics of horizontal tail, because downwash reduces an angle of attack of horizontal tail. If the aircraft angle of attack , an angle of attack of horizontal tail with taking into account an angle of downwash will be

. (14.2)

The value of angle of downwash depends on the wing plan form, angle of its setting, wing and fuselage interference, angle of attack, number , and coordinates of the considered point. The significant influence on the angle of downwash is paid by vortexes forming at flow about wing on its lateral and leading edges.

Disturbances are distributed in all parties at subsonic speeds, therefore tail unit effects on flow about the wing, located before it. However this influence, as a rule, is insignificant in comparison with wing influence onto flow about tail unit located behind. The wing downwash also reduces an angle of attack of that fuselage part which is located behind a wing.

Disturbances are not distributed forward against flow at supersonic speeds, the area of their propagation is limited by cones of disturbances and shock waves. That is why there can be zones in which there is no downwash at supersonic speeds.

Fig. 14.5. Dependence of derivative of downwash on number

The angle of downwash depends on wing lift, therefore, from an angle of attack. For linear site this dependence can be written as

. (14.3)

The derivative of downwash by the angle of attack depends on number , how it is shown in fig. 14.5. At subsonic speeds the lifting properties of the wing grow at increasing of number , the derivative increases also. They drop at supersonic speeds with increasing of number , besides, the zones of disturbances propagation are narrowing, therefore derivative reduces.

If the mean angle of downwash is known, then the angle of attack of horizontal tail is calculated under the formula . For the aircraft of the normal configuration the parameter is called as factor of tail-plane effectiveness. The angle of downwash is determined by aerodynamic and geometrical twist of wing.

The configuration of horse-shoe vortex is used as the basis for calculation of downwash, that is right, because the vortex sheet is unstable and at some distance is turned off in two tip vortexes.

The remarks:

1. Generally downwash is variable spanwise. However, at calculation of the total aerodynamic characteristics of the trailing lifting surface in the aerodynamic configuration the mean value of downwash spanwise. Obviously, the downwash before a wing will be less in the canard configuration, as wing external parts falls into the upwash.

2. In the aircraft system the components of downwash and also will depend on mutual arrangement of the leading and trailing lifting surfaces, shape and geometry of cross section of the leading lifting surface with a fuselage, numbers . The fuselage influence onto downwash is taken into account by change of the configuration of the horse-shoe vortex.

3. The additional sources of downwash can be the jets of the air prop and jet engines which turbulent baffling and ejection properties create a field of speeds directed to jet axis.

Using model of horse-shoe vortex it is possible to offer the following formula for calculation of components of angle of downwash caused by system: lifting surface-fuselage:

, (14.4)

where and - aspect ratio and derivative of the lift coefficient of forward surface cantilevers. The multipliers which are included in (14.4), depend on aerodynamic configuration of the aircraft and Mach numbers .

The multiplier takes into account mutual arrangement of a wing and horizontal tail fuselage lengthwise. The multiplier takes into account vertical displacement of horizontal tail relatively to wing. The multiplier is connected to aerodynamic configuration of the aircraft (for normal configuration ). The multipliers and also take into account the influence of fuselage onto downwash and depend on the shape of cross section a forward lifting surface - fuselage.